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Simplifying (4x + 6)(7 + 8x + 24) = 0 Reorder the terms: (6 + 4x)(7 + 8x + 24) = 0 Reorder the terms: (6 + 4x)(7 + 24 + 8x) = 0 Combine like terms: 7 + 24 = 31 (6 + 4x)(31 + 8x) = 0 Multiply (6 + 4x) * (31 + 8x) (6(31 + 8x) + 4x * (31 + 8x)) = 0 ((31 * 6 + 8x * 6) + 4x * (31 + 8x)) = 0 ((186 + 48x) + 4x * (31 + 8x)) = 0 (186 + 48x + (31 * 4x + 8x * 4x)) = 0 (186 + 48x + (124x + 32x2)) = 0 Combine like terms: 48x + 124x = 172x (186 + 172x + 32x2) = 0 Solving 186 + 172x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(93 + 86x + 16x2) = 0 Factor a trinomial. 2((31 + 8x)(3 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + 8x)' equal to zero and attempt to solve: Simplifying 31 + 8x = 0 Solving 31 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 8x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 8x = 0 + -31 8x = 0 + -31 Combine like terms: 0 + -31 = -31 8x = -31 Divide each side by '8'. x = -3.875 Simplifying x = -3.875Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-3.875, -1.5}
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